Those lyrics from the title song of Bettye LaVette’s new album, “Worthy,” were not written by Ms. LaVette, one of the greatest of all soul singers. But as she proudly growled them out on Friday evening at Café Carlyle, they rang with the conviction of someone who had emerged unbowed from a lifetime of setbacks. It was hard to imagine that anyone else could have written them.

Ms. LaVette, 69, doesn’t need to write her own material. Whatever she sings acquires the fierce, confessional intensity of someone who barely lived to tell the tale. Her particular triumph is the belated recognition over the last decade that she is the artistic equal of soul music giants like Otis Redding and Tina Turner. Despite some minor hits, starting when she was a teenager in the early ’60s, Ms. LaVette had to wait almost half a century for her moment to come.

Her ups and downs are bluntly described in her 2012 autobiography, “A Woman Like Me,” written with David Ritz. The personal reward for her persistence is hard-won self-esteem. In the words of that title song, “Worthy, worthy, what a thing to claim/Worthy, worthy ashes into flame.”

With a band led by Alan Hill on piano, that included Darryl Pierce on drums, Brett Lucas on guitar, and James Simonson on bass, the music was raw, stripped-down rhythm and blues, and her singing was devoid of vocal frills, the better to cut to the heart of the matter. Lesser-known songs by the Beatles (“Wait”), the Rolling Stones (“Complicated”) and Bob Dylan (“Unbelievable”) were reconceived as blues-based confessions over lean, taut arrangements that didn’t waste a note.

Ms. LaVette performed the album from start to finish. Besides “Worthy,” the killer song was James H. Brown Jr.’s “Just Between You and Me and the Wall, You’re a Fool,” a devastating indictment of a selfish, heartless partner. By the end of the evening, the ashes of Ms. LaVette’s hard life had reignited, and there was fire in the air.